To add to the kids list, I also carry:
Small (8x10) tarp
Framing hammer
Stanley shortcut saw
Tie wire
Zip ties
Wd40
1lb proane torch
In the non-frozen months, baby wipes and/or hand cleaning wipes
Couple rolls of blue shop towels
Channel locks, needle nose, wire cutters and a 4-way screwdriver in one of thie small Klein tools pouches under the drivers seat. I use those all the time. Should throw a small crescent wrench in there too.
I have taken to carrying the hi lift in addition to a bottle jack.
I carry a pretty decent tool set with 1/4, 3/8, and 1/2" sockets/ratchets, wrenches and screwdrivers. Probably overkill, but having it with me has saved me a lot of grief.
I carry two 30k tow straps instead of chain, but chain could certainly be handier in some cases.